A glossary is provided below of the terms used in connection with the invention described herein.
ABS=Amplitude beamsplitter. PA0 D=Sensitivity and gain of square-law detector. PA0 D.sup.2 =Square-law detector. PA0 DA=Differential amplifier. PA0 DL=Delay line. PA0 E=Electric field vector of signal light beam (E=E.sub.x +E.sub.y). PA0 i=Electric current. PA0 L=Electric field vector of local oscillator light beam (L=L.sub.x +L.sub.y). PA0 P=Polarizer (absorbs or reflects the orthogonal polarization.) PA0 PBS=Polarization beamsplitter. PA0 PMM=Polarization matching mixer. PA0 PS=Phase shifter (changes phase .delta. between x- and y-components of E). PA0 R=Rotator (half-wave retarder used to rotate polarization vector.) PA0 S=Output signal (usually in decibles.) PA0 T=Amplitude throughput (can be transmittance or reflectance.) PA0 U=Amplitude transmittance. PA0 V=Amplitude reflectance. PA0 .alpha.=Arc tan A.sub.y /A.sub.x, where A.sub.x and A.sub.y are amplitude components (0.ltoreq..alpha..ltoreq.90.degree.). PA0 .delta.=Fixed phase term in frequency argument of field vector (-.pi..ltoreq..delta.&gt;.pi.). PA0 .omega.=Optical frequency in radians per second (.omega..sub.E and .omega..sub.L).
The superscript arrow ( ) indicates an electromagnetic vector quantity containing the time-dependent term cos (.omega.t+.delta.).
The signal from a modulated beam of light E may have any polarization state, and may be represented by its x- and y-components, EQU E.sub.x =E cos .alpha..sub.E =E cos .alpha..sub.E cos (.omega..sub.E t+.delta..sub.Ex)
and EQU E.sub.y =E sin .alpha..sub.E =E sin .alpha..sub.E cos (.omega..sub.E t+.delta..sub.Ey). (1)
The polarization state is defined by .delta.=.delta..sub.Ex -.delta..sub.Ey and .alpha..sub.E. If .delta.=0 or .pi., the light is linearly polarized for all values of .alpha..sub.E. If .delta.=.+-..pi./2 and .alpha..sub.E =45.degree., the light is circularly polarized. Any other combination of .delta. and .alpha..sub.E indicates elliptically polarized light. Equation (1) represents the signal carrier. The data signal modulation may appear on E, .omega..sub.E or .delta..
Coherent detection of modulated light requires the mixing of the signal beam E with a local oscillator beam L in such a way that the two wavefronts are parallel to within a small fraction of a wave and the polarization vector match. The local oscillator L is linearly polarized (.delta..sub.Lx =.delta..sub.Ly=.delta..sub.L) in the preferred embodiments of this invention, and it will be so assumed during the description. Other forms of polarization are possible, so long as E and L are orthogonal or matching where called for in the description. The local oscillator may be represented by its x- and y-components, EQU L.sub.x =L cos .alpha..sub.L =L cos .alpha..sub.L cos (.omega..sub.L t+.delta..sub.L)
and EQU L.sub.y =L sin .alpha..sub.L =L sin .alpha..sub.L cos (.omega..sub.L t+.delta..sub.L). (2)
The local oscillator frequency .omega..sub.L will differ from .omega..sub.E for heterodyne detection, and will match .omega..sub.E for homodyne detection. In most cases, .alpha..sub.L will be either 0.degree. or 45.degree..
The signal beam resulting from mixing E and L is focussed on a square-law detector whose output current i is proportional to the intensity (square of the amplitude) of the incident light: ##EQU1## where D is a constant proportional to the product of the sensitivity and gain of the detector. The term 2EL may be expanded to give ##EQU2## Only the difference frequency .omega..sub.E -.omega..sub.L is of interest for heterodyne and homodyne detection. The sum frequency component .omega..sub.E +.omega..sub.L is therefore eliminated by filtering. The net output current is thus EQU i=D{E.sup.2 +L.sup.2 +EL cos [(.omega..sub.E -.omega..sub.L)t+(.delta..sub.E -.delta..sub.L)]} (5)
The ultimate measure of performance in an optical system of this type is signal-to-noise ratio. Noise arises from a number of sources, one of which is photon shot noise, the statistical variation of the arrival time and detection of photons in a nominally uniform beam of light. In heterodyne and homodyne detection devices, the local oscillator is usually strong enough so that photon shot noise is the dominant noise source. All terms in equation (5) contribute to photon shot noise, but only the difference frequency term contributes to signal. Since E.sup.2 and L.sup.2 contribute only to noise, they will be eliminated by differential detection.
In differetial detection, E.sup.2 and L.sup.2 are eliminated by splitting E and L equally, forming E.sub.+, E.sub.-, L.sub.+ and L.sub.-, and sending them in pairs to two square-law detectors, one detector seeing the sum pair E.sub.+ +L.sub.+, the other seeing the difference pair E.sub.- -L.sub.-. This produces two signal currents i.sub.+ and i.sub.-, EQU i.sub.+ =D.sub.+ {.sub.+.sup.2 +L.sub.+.sup.2 +E.sub.+ L.sub.+ cos [(.omega..sub.E -.omega..sub.L)t+(.delta..sub.E -.delta..sub.L)]}(6) EQU i.sub.- =D.sub.- {E.sub.-.sup.2 +L.sub.-.sup.2 -E.sub.- L.sub.- cos [(.omega..sub.E -.omega..sub.L)t+(.delta..sub.E -.delta..sub.L)]}(7)
If D.sub.+ =D.sub.- =D, E.sub.+ =E.sub.- =E.sub.d and L.sub.+ =L.sub.- =L.sub.d, subtracting i.sub.- from i.sub.+ in a differential amplifier cancels the E.sup.2 and L.sup.2 terms, leaving a net current
i=i.sub.+ -i.sub.- =2DE.sub.d L.sub.d cos [(.omega..sub.E -.omega..sub.L)t+(.delta..sub.E -.delta..sub.L)] (8)
The difference frequency .omega..sub.i =.omega..sub.E -.omega..sub.L is usually referred to as the intermediate frequency in describing heterodyne detector systems. In homodyne detector systems, .omega..sub.L =.omega..sub.E, so that .omega..sub.i =0. In this case, equation (8) takes the special form EQU i=2DE.sub.d L.sub.d cos (.delta..sub.E -.delta..sub.L) (8')
In heterodyne detection, the intermediate frequency .omega..sub.i forms a radio frequency carrier which is processed by standard radio frequency demodulation techniques to extract the data signal. In homodyne detection, the data signal is obtained directly from the detector output current.
In both heterodyne and homodyne detection, the signal current passes through a resistive load r, generating a voltage v, where v=ir. The signal S used in signal-to-noise ratio calculations is the power generated by this process, S=vi=i.sup.2 r. The electronic processing by which the signal is extracted is not the subject of this invention beyond the extent to which it is described herein. In using the signal S to compare performance of the apparatus of this invention to prior art, the signal S will be given by EQU S=4CD.sup.2 E.sub.d.sup.2 L.sub.d.sup.2 ( 9)
where C is a constant representing electronic signal processing, C being assumed to be the same for all systems being compared, unless otherwise noted. The quantity 4E.sub.d.sup.2 L.sub.d.sup.2 is the quantity of interest for optical performance comparisons, since it is affected by the throughput efficiency of the optical collecting system, which the apparatus of this invention is intended to improve. Note that this quantity is the same whether heterodyne of homodyne detection is used.
FIG. 1 is a block diagram representing the generic principals of the mixing and splitting technique currently used for detecting light coherently by heterodyne and homodyne differential detection. The modulated signal E and local oscillator signal L enter the mixer 10 from the signal source SO and local oscillator LO, and produce an output E.sub.1 +L.sub.1. E.sub.1 and L.sub.1 are linearly polarized in orthogonal directions, and in general their amplitudes E.sub.1 and L.sub.1 will be reduced. A splitter 12 receives and divides the signal and local oscillator into two equal pairs E.sub.d and L.sub.d. In the process, a phase shaft of 180.degree. is added to .delta..sub.L for the difference channel (line 14). This is equivalent to changing the signal of L.sub.d, so that in the difference channel, L.sub.d is subtracted from E.sub.d, and in the sum channel (line 16), L.sub.d is added to E.sub.d. The square law detector D.sup.2.sub.+ (18) detects the mixed light signal in the sum channel, producing the current i.sub.+. The square law detector D.sup.2.sub.- (20) detects the mixed light signal in the difference channel, producing the current i.sub.-. The detector output currents i.sub.+ and i.sub.- are subtracted in the differential amplifier DA to produce the net output current i.
In the typical optical communications system, the signal oscillator SO is a remotely located device whose frequency cannot be relied on to have the exact value needed to match the frequency of the local oscillator LO for homodyne detection, or to produced the desired intermediate frequency .omega..sub.i for heterodyne detection. It is therefore necessary to control LO to match the frequency of the local oscillator signal L to the value required for homodyne or heterodyne detection of the incoming signal E. To do this, portions of i.sub.+ and i.sub.- are split off and fed to frequency sensor 22. In this device, the signal currents are passed through narrow bandpass filters to strip the data signal, allowing the intermediate frequency .omega..sub.i to be extracted. This is used to generate a frequency control signal FC, which is fed to the local oscillator. This feature is common to all coherent detection systems discussed here and does not enter directly into optical efficiency calculations.
FIG. 2 represents prior art in the form of Henning's Balanced Optical Demodulator, U.S. Pat. No. 3,694,656. In FIG. 2, a first amplitude beamsplitter (ABS.sub.1) is used to mix and split the signal E from SO and the local oscillator L from LO. (An amplitude beamsplitter is a device which divides the amplitude of the light incident on it into two components, one of which is reflected, and the other transmitted. The ABS may be a thin metallic coating on a glass substrate, or it may be a multilayer dielectric coating on a glass substrate.) Prior to mixing, the signal E first passes through a polarizer P.sub.1 to eliminate components which cannot interfere with the local oscillator. As a result, E.sub.1 =E cos .alpha..sub.E, where .alpha..sub.E is measured relative to the polarization axis of P.sub.1. L passes through a rotator R which rotates its polarization vector so that L.sub.1 is polarized orthogonal to E.sub.1. The losses associated with rotation by R are small enough so that one may assume that L.sub.1 =L. (Losses associated with glass path and air-glass interfaces will be ignored in comparing the present invention to prior art, since they are small in comparison to other factors which will be considered, and they are roughly equal in all systems under consideration.)
ABS.sub.1 is characterized by an amplitude transmittance U.sub.1 and amplitude reflectance V.sub.1. Thus the outputs of ABS.sub.1, i.e. E.sub.2 and L.sub.2, are as follows: E.sub.2 =U.sub.1 E cos .alpha..sub.E and L.sub.2 =V.sub.1 L, and E.sub.2 and L.sub.2 are orthogonally polarized. Note that the small arrows above the lines in FIG. 2 represent the polarization direction as seen looking toward the source.
The orthogonally polarized signals E.sub.2 and L.sub.2 are coupled to ABS.sub.2, which is characterized by amplitude transmittance U.sub.2 and amplitude reflectance V.sub.2. After passing through ABS.sub.2, E.sub.2 and L.sub.2 are broken up into a sum pair E.sub.3+ and L.sub.3+, and a difference pair, E.sub.3- and L.sub.3-, where E.sub.3+ =EU.sub.1 U.sub.2 cos .alpha..sub.E, L.sub.3+ =LV.sub.1 U.sub.2, E.sub.3- =EU.sub.1 V.sub.2 cos .alpha..sub.E and L.sub.3- =LV.sub.1 V.sub.2. Each pair is passed through a respective polarizer (P.sub.2+ or P.sub.2-) which will transmit components of each pair which can interfere with each other. These components ae polarized at 45.degree. to the initial polarization of E.sub.3 and L.sub.3, so the amplitude of each will be reduced by cos 45.degree.. The effects of P.sub.2+ and P.sub.2- on phase are more important: P.sub.2+ adds .pi./2 to .delta..sub.L+ and subtracts .pi./2 from .delta..sub.E+, which rotates the field vectors toward each other; P.sub.2- subtracts .pi./2 from .delta..sub.L- and adds .pi./2 to .delta..sub.E-, which rotates the field vectors away from each other. As a result, at a point in time when E.sub.d+ and L.sub.d+ have the same sign, and thus add, E.sub.d- and L.sub.d- have the opposite sign, and thus subtract.
Thus there are two mixed fields incident on each detector, EQU E.sub.d+ =EU.sub.1 U.sub.2 cos 45.degree. cos .alpha..sub.E ( 10) EQU L.sub.d+ =LV.sub.1 U.sub.2 cos 45.degree. (11)
incident on D.sup.2.sub.+, and EQU E.sub.d- =EU.sub.1 V.sub.2 cos 45.degree. cos .alpha..sub.E ( 12) EQU L.sub.d- =LV.sub.1 V.sub.2 cos 45.degree. (13)
incident on D.sup.2.sub.-. With equal detector sensitivities D, the condition for difference detection is that E.sub.d+ =E.sub.d- =E.sub.d and L.sub.d+ =L.sub.d- =L.sub.d. Equations (10)-(13) show the condition for this to be U.sub.2 =V.sub.2. Comparison to equations (8) and (9) indicates that U.sub.1.sup.2 V.sub.1.sup.2 will appear in the signal level. Since U.sup.2 +V.sup.2 =C.sub.t .ltoreq.1.0 for all ABSs, it can be shown that the maximum signal level will be achieved when U.sub.1 =V.sub.1. Assume that U.sub.1 =V.sub.1 =U.sub.2 =V.sub.2 =T. Then U.sup.2 +V.sup.2 =2T.sup.2 =C.sub.t .ltoreq.1.0, and it follows T.ltoreq.2.sup.-1/2.
By analogy to equations (3) through (9), the output current i from DA for FIG. 2 is EQU i=2DELT.sup.4 cos.sup.2 45.degree. cos .alpha..sub.E cos [(.omega..sub.E -.omega..sub.L)t+(.delta..sub.E -.delta..sub.L)] (14)
and the signal S is EQU S=4CD.sup.2 E.sup.2 L.sup.2 T.sup.8 cos.sup.4 45.degree. cos.sup.2 .alpha..sub.E .ltoreq.(CD.sup.2 E.sup.2 L.sup.2 cos.sup.2 .alpha.)/16 (15)
There are two factors degrading performance in FIG. 2, one (T.sup.8) associated with the light losses in the amplitude beamsplitter, and the other (cos.sup.2 .alpha..sub.E) associated with the sensitivity of the detector to the polarization of the incoming signal. Accordingly, a need exists for a coherent light detection system which minimizes the light loss attributable to amplitude beamsplitters and the sensitivity of the detector to changes in the polarization of the light signal.